### 2019　Advanced topics in Analysis H

Font size  SML

Academic unit or major
Graduate major in Mathematics
Instructor(s)
Ninomiya Syoiti
Course component(s)
Lecture
Day/Period(Room No.)
Thr3-4(H137)
Group
-
Course number
MTH.C504
Credits
1
2019
Offered quarter
2Q
Syllabus updated
2019/3/18
Lecture notes updated
2019/7/29
Language used
English
Access Index

### Course description and aims

In this lecture, the topics discussed in ``Advanced topics in analysis G'' are developed in continuous time models.

The following notions such as Ito integral, Stochastic Differential Equations, and some models in mathematical finance are discussed.

### Student learning outcomes

Understanding the following notions:
Ito calculus and basic knowledge of stochastic differential equations

### Keywords

Ito calculus, stochastic differential equation, mathematical finance

### Competencies that will be developed

 Intercultural skills Communication skills ✔ Specialist skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

Blackboard and handouts

### Course schedule/Required learning

Course schedule Required learning
Class 1 Ito integral (stochastic integral)(1), definition Details will be provided each class session.
Class 2 Ito integral (2), basic properties
Class 3 Ito formula
Class 4 Ito Representation theorem
Class 5 Stochastic Differential Equation (1), Existence of the solution
Class 6 Stochastic Differential Equation (2), Approximations of solutions
Class 7 Stochastic Differential Equation (3)
Class 8 Mathematical Finance

### Textbook(s)

None in particular.

### Reference books, course materials, etc.

Taniguchi, S., ``Stochastic Differential Equations,'' Kyoritsu
Kusuoka, S., ``Stochastic Analysis,'' Chisenshokan

### Assessment criteria and methods

Based on reports. Details will be provided in the class.

### Related courses

• MTH.C361 ： Probability Theory
• MTH.C503 ： Advanced topics in Analysis G

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

None in particular

### Other

None in particular